Ch. 5 Gases

Ch. 5 Topics Kinetic Molecular Theory and Gases Ideal vs. Real Gases What conditions are ideal for gases? PV=nRT PV=(m/MM)RT Know how to convert C to K Density and gases and MW kitty cat Graham’s Law of Effusion Molar volume of any gas at STP= 22.4 L/mol STP= 0°C (273 K) and 1 atm=760 mm Hg = 760 torr Combined Gas Law P 1 V 1 =P 2 V 2 T 1 T 2 Boyles Law P 1 V 1 =P 2 V 2 Charles’ Law V 1 /T 1 = V 2 /T 2 Gay Lussac’s Law P 1 /T 1 = P 2 /T 2 Avogadro’s Law or n is proportional to L or volume Molar Volume of a Gas Lab Dalton’s Law of Partial Pressures (P total = P 1 + P 2 + P 3 + P 4 …..) Mole fraction (it is really a mole decimal and no units) Barometric pressure and manometers Kinetic energy and as a function of temperature **Sig Figs and Units!**

Gases Refresher: (KMT to come) o Uniformly fills any container o Easily compressible o Mixes (diffuses) completely with other gases Pressure and Units o Pressure = Force/Area o SI Unit is Pascal (Pa) 1 Pa = 1kg/ms 2 = 1N/m 2 1 atm = 101,325 Pa 1 atm = 760 torr = 760 mmHg = inHg = 14.7 lb/in 2

Pressure Conversions The pressure exerted by a gas is measured to be atm. Convert this pressure to torr and pascals.

Boyle’s Law The pressure exerted by a gas is inversely proportional to the volume the gas occupies. Mathematical Relationship P 1 V 1 = P 2 V 2 Temperature (T) is held constant. Amount (n) is held constant. A gas that strictly obeys Boyle’s law is called an ideal gas.

Boyle’s Law The volume of a given amount of gas held at constant temperature varies inversely with the pressure. EQUATION: P 1 V 1 = P 2 V 2 1 Denotes Initial Conditions 2 Denotes New (Final) Conditions

Boyle’s Law

Volume vs. Pressure Sketch *As pressure increases, the volume…

Steps to Solve Problems GUESS Method 1.Givens (check units) 2.Unknown (destination) 3.Equation (isolate unknown) 4.Substitute (plug-in known values) 5.Solve *Keep track of units!!*

Boyle’s Example A gas has a pressure of 3.2atm and occupies a volume of 45L. What will the pressure be if the volume is compressed to 27 L at a constant temperature?

Boyle Practice A sample tube containing mL of CO gas at 20.6 torr is connected to an evacuated 1.13 L flask. What will the pressure be when the CO is allowed into the flask? 1.89 torr

Charles’s Law Studied the relationship between volume (V) and temperature (T) of a gas. At a given pressure (P), volume (V) and temperature (T) are directly related.

Temperature vs. Volume

Charles’s Law At a given pressure, volume and temperature are directly related. EQUATION: Temperature MUST BE in KELVIN!! 1 Denotes Initial Conditions 2 Denotes New (Final) Conditions

Conversion Temperature Must be in Kelvin!!! T K = T C

Volume vs. Temperature Sketch *As temperature increases, the volume…

Absolute Zero 0 K o Would result in a negative volume o Temperatures of about K have been reached in laboratories

Let’s Practice (Hint: GUESS method) A gas at 89˚C occupies a volume of 0.67 L. At what Celsius temperature will cause the volume to increase to 1.12L?

Let’s Practice (Hint: GUESS method) What is the volume of the air in a balloon that occupies 0.620L at 25 ˚C if the temperature is lowered to 0.00 ˚C ?

Gay-Lussac’s Law Video Demo Studied the relationship between temperature (T) and pressure (P) of a gas. At a given volume, temperature and pressure are directly related.

Gay-Lussac’s Law At a given volume, pressure and temperature are directly related. EQUATION: Temperature MUST BE in KELVIN!! 1 Denotes Initial Conditions 2 Denotes New (Final) Conditions

Temperature vs. Pressure

Pressure vs. Temperature Sketch *As temperature increases, the pressure…

Let’s Practice (Hint: GUESS method) The pressure in an automobile tire is 1.88 atm at 25.0˚C. What will be the pressure if the temperature warms up to 37.0˚C?

Let’s Practice (Hint: GUESS method) If a gas sample has a pressure of 30.7 kPa at 0.00˚C, by how much does the temperature have to decrease to lower the pressure to 28.4 kPa?

Avogadro’s Law A gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas. 1 Denotes Initial Conditions 2 Denotes New (Final) Conditions

Avogadro’s Example A 5.20 L sample at 18.0 C and 2.00 atm pressure contains moles of a gas. If we add an additional 1.27 moles of the gas at the same temperature and pressure, what will be the total volume occupied by the gas?

Avogadro’s Practice An 11.2 L sample of gas is determined to contain 0.50 moles of N 2. At the same temperature and pressure, how many moles of gas would there be in a 20. L sample?

Avogadro’s Principle Gas particles vary in size The kinetic theory (5 postulates) states particles in a gas sample are far enough apart that size has a negligible (little) influence on volume occupied by a fixed number of particles. What does this mean? Avogadro’s principle: equal volumes of gases at the same temperature and pressure contain equal number of particles.

Recall: 1 mole = 6.02 x particles (atoms) Molar volume: volume one mole of gas occupies at standard temperature and pressure (STP)

Standard Temperature and Pressure (STP) Standard temperature and pressure = 0.00 C and 1.00 atm One mole of any gas will occupy 22.4 L (volume) at STP. Conversion: 22.4 L 1 mol

Practice Problem (Hint: use conversion factor from previous slide) Determine the volume of a container that holds 8.90 mol of gas at STP. What size container do you need to hold 0.62 mol of Cl 2 gas at STP?

Ideal Gas Law This law describes an ideal gas’s physical behavior in terms of all four variables. Four variables! Describe on a molecular level, why a car tire appears flat in cold temperatures. Describe why a car tire increases in volume as air is added to the tire (increase moles/amount).

Ideal Gas Law

PV = nRT What is R? R = ideal gas constant -The value was determined experimentally. -Look at the units. The units tell you what the other variables MUST be in!

Conversion Reminder Temperature Must be in Kelvin!!! T K = T C

Real Gas vs Ideal Gas Real Gas: NO gas is ideal. Gases do have volume and they do have attractive forces. Ideal Gas: Gas particles do not attract one another. Gas particles take up no space.

Why do we use the ideal gas law? For most conditions, calculations made using PV = nRT approximate what actually occurs in experiments. It does not work well when the gas is under high pressure or low temperatures

Steps to Solve Problems GUESS Method 1.Givens (check units) Temperature MUST be in Kelvin!! (if not convert) T K = T C 2.Unknown (destination) 3.Equation (isolate unknown) 4.Substitute (plug-in known values) 5.Solve *Keep track of units!!*

Example (Hint: just …GUESS ) If the pressure exerted by a gas at 25˚C in a volume of L is 3.81 atm, how many moles of gas are present?

Example (Hint: just …GUESS ) A sample of methane gas (CH 4 ) at atm and 4.0 C occupies a volume of 7.0 L. What volume will the gas occupy if the pressure is increased to 1.52 atm and the temperature increased to 11.0 C?

Let’s Practice (Hint: just …GUESS ) Determine the Celsius temperature of 2.49 moles of gas contained in a 1.00 L vessel at a pressure of 143 kPa.

Let’s Practice (Hint: just …GUESS ) Calculate the volume that a mol sample of a gas will occupy at 265 K and a pressure of atm.

Individual Practice Complete the following problems (page 219) o 27, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, and 49